Proof of the Hyperplane Zeros Conjecture of Lagarias and Wang

We prove that a real analytic subset of a torus group that is contained in its image under an expanding endomorphism is a finite union of translates of closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and Wang for real analytic varieties. Our proof uses real analytic geometry, topological dynamics and Fourier analysis.Comment: 25 page

Search for two-neutrino double electron capture on 124^{124}Xe with the XMASS-I detector

Double electron capture is a rare nuclear decay process in which two orbital electrons are captured simultaneously in the same nucleus. Measurement of its two-neutrino mode would provide a new reference for the calculation of nuclear matrix elements whereas observation of its neutrinoless mode would demonstrate lepton number violation. A search for two-neutrino double electron capture on $^{124}$Xe is performed using 165.9 days of data collected with the XMASS-I liquid xenon detector. No significant excess above background was observed and we set a lower limit on the half-life as $4.7 \times 10^{21}$ years at 90% confidence level. The obtained limit has ruled out parts of some theoretical expectations. We obtain a lower limit on the $^{126}$Xe two-neutrino double electron capture half-life of $4.3 \times 10^{21}$ years at 90% confidence level as well.Comment: 6 pages, 3 figures, accepted for publication in Physics Letters

Scintillation-only Based Pulse Shape Discrimination for Nuclear and Electron Recoils in Liquid Xenon

In a dedicated test setup at the Kamioka Observatory we studied pulse shape discrimination (PSD) in liquid xenon (LXe) for dark matter searches. PSD in LXe was based on the observation that scintillation light from electron events was emitted over a longer period of time than that of nuclear recoil events, and our method used a simple ratio of early to total scintillation light emission in a single scintillation event. Requiring an efficiency of 50% for nuclear recoil retention we reduced the electron background to 7.7\pm1.1(stat)\pm1.2 0.6(sys)\times10-2 at energies between 4.8 and 7.2 keVee and to 7.7\pm2.8(stat)\pm2.5 2.8(sys)\times10-3 at energies between 9.6 and 12 keVee for a scintillation light yield of 20.9 p.e./keV. Further study was done by masking some of that light to reduce this yield to 4.6 p.e./keV, the same method results in an electron event reduction of 2.4\pm0.2(stat)\pm0.3 0.2(sys)\times10-1 for the lower of the energy regions above. We also observe that in contrast to nuclear recoils the fluctuations in our early to total ratio for electron events are larger than expected from statistical fluctuations.Comment: 25 pages, 15 figure

Resolving theta_{23} Degeneracy by Accelerator and Reactor Neutrino Oscillation Experiments

If the lepton mixing angle theta_{23} is not maximal, there arises a problem of ambiguity in determining theta_{23} due to the existence of two degenerate solutions, one in the first and the other in the second octant. We discuss an experimental strategy for resolving the theta_{23} octant degeneracy by combining reactor measurement of theta_{13} with accelerator nu_{mu} disappearance and nu_{e} appearance experiments. The robustness of the theta_{23} degeneracy and the difficulty in lifting it only by accelerator experiments with conventional nu_{mu} (and nu_{mu}-bar) beam are demonstrated by analytical and numerical treatments. Our method offers a way to overcome the difficulty and can resolve the degeneracy between solutions sin^2 theta_{23} = 0.4 and sin^2 theta_{23} = 0.6 if sin^2 (2 theta_{13}) \gsim 0.05 at 95% CL by assuming the T2K phase II experiment and a reactor measurement with an exposure of 10 GW.kt.yr. The dependence of the resolving power of the octant degeneracy on the systematic errors of reactor experiments is also examined.Comment: 23 pages, 9 figures, version to appear in PR

On two-dimensional surface attractors and repellers on 3-manifolds

We show that if $f: M^3\to M^3$ is an $A$-diffeomorphism with a surface two-dimensional attractor or repeller $\mathcal B$ and $M^2_ \mathcal B$ is a supporting surface for $\mathcal B$, then $\mathcal B = M^2_{\mathcal B}$ and there is $k\geq 1$ such that: 1) $M^2_{\mathcal B}$ is a union $M^2_1\cup...\cup M^2_k$ of disjoint tame surfaces such that every $M^2_i$ is homeomorphic to the 2-torus $T^2$. 2) the restriction of $f^k$ to $M^2_i$ $(i\in\{1,...,k\})$ is conjugate to Anosov automorphism of $T^2$